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RESEARC H ARTIC L E Open Access
An application of principal component analysis to
the clavicle and clavicle fixation devices
Zubin J Daruwalla
1*
, Patrick Courtis
2
, Clare Fitzpatrick
2
, David Fitzpatrick
2
, Hannan Mullett
1
Abstract
Background: Principal component analysis (PCA) enables the building of statistical shape models of bones and
joints. This has been used in conjunction with computer assisted surgery in the past. However, PCA of the clavicle
has not been performed. Using PCA, we present a novel method that examines the major modes of size and
three-dimensional shape variation in male and female clavicles and suggests a method of grouping the clavicle
into size and shape categories.
Materials and methods: Twenty-one high-resolution computerized tomography scans of the clavicle were
reconstructed and analyzed using a specifically developed statistical software package. After performing statistical
shape analysis, PCA was applied to study the factors that account for anatomical variation.
Results: The first principal component representing size accounted for 70.5 percent of anatomical variation. The
addition of a further three principal components accounted for almost 87 percent. Using statistical shape analysis,
clavicles in males have a greater lateral depth and are longer, wider and thicker than in females. However, the
sternal angle in females is larger than in males. PCA confirmed these differences between genders but also noted
that men exhibit greater variance and classified clavicles into five morphological groups.
Discussion And Conclusions: This unique approach is the first that standardizes a clavicular orientation. It
provides information that is useful to both, the biomedical engineer and clinician. Other applications include
implant design with regard to modifying current or designing future clavicle fixation devices. Our findings support
the need for further development of clavicle fixation devices and the questioning of whether gender-specific

devices are necessary.
Introduction
The selection of an y orthopaedic fixation implant is dri-
ven by several factors. However, the shape of the bone
involved is commonly overlooked. When selecting a cla-
vicular implant, there are several factors that drive the
decision but the morphology of the clavicle is rarely
considered. Experience to date has shown that linear
scaling is a dominant mode of variation in human anat-
omy [1]. This paper builds on geometric data and meth-
odology presented in a previous study analyzing linear
measurements [2] in order to provide detailed informa-
tion relating to the modes of variation in three-dimen-
sional (3D) shape that occur in the clavicle. It must be
noted that while intramedullary and plate fixation are
accepted and widely used methods of treatment for
fractures of the clavicle, current clavicular implants
overlook the variations in geometry of the bone. As the
clavicle demonstrates a complex anatomy, it is vital to
understand the variations not only in size but a lso
shape. This allows optimization of the implant design,
in turn ensuring effective fracture fixation. This is the
first 3D study that examines the shape variation of the
clavicle and suggests a metho d of grouping the clavicle
into size and shape categori es based on statist ical shape
and principal component analyses.
Materials
Ethics approval for this study was sought and granted
through the Royal College of Surgeons in Ireland
Research Ethics Committee (Study No. REC 401).

Fif teen fresh froz en shoulder specimens previously used
for a shoulder course and consented for research pur-
poses were scanned using high-resolution (0.625 mm)
* Correspondence:
1
Department of Orthopaedic Surgery, Beaumont Hospital, Dublin, Republic
of Ireland
Daruwalla et al. Journal of Orthopaedic Surgery and Research 2010, 5:21
/>© 2010 Daruwalla et al; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative
Commons Attribution License (http:/ /creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and
reproduction in any medium, provided the original work is proper ly cited.
computerized tomography (CT). These specimens were
stored in a freezer compartment in airtight bags for two
months after the course and defrosted for 24 hours
prior to being scanned. Surrounding soft tissue was not
removed.Oneclaviclewasfoundtobefractured,and
five were incomplete so were excluded. A further 16
high-resolution CT scans of the clavicle were obtained
by searching the hospital database but four were
excluded because they did not include either the super-
ior or inferior medial or lateral aspects completely. In
order to ensure none of the clavicles had pathology,
search criteria included patients who had a CT scan
performed for imaging of the proximal humerus or sca-
pula. The study comprised a total of 21 clavicles.
Six of the scans were from males and 15 from females,
with an average age of 54 (range 20-85 years). Twelve
were from the left side and nine from the right. Biodata
was available in all cases and cause of death in the
group of fresh frozen specimens was known. None of

the 21 clavicles scanned showed signs of a previous
fracture.
All CT scans were reconstructed using Mimics soft-
ware (Materialise b.v., Leuven, Belgium). These images
were subsequently imported as three-dimensional (3D)
STL files into Arthron, a statistical software package
specifically developed by the Department of Mechanical
Engineering in the institution where our research was
being conducted.
Methods
Clavicular Coordinate Frame
The coordinate systems of the STL files were in the ori-
ginal coordinate frame of the CT scanner. This was
redefined using Arthron and applied to all the files. As
previously described [2], multiple points on the supero-
lateral flattest surface of the clavicle were selected
(Figure 1). A best fit plane was then defined to fit these
points (Figure 2). Two points representing the medial
and lateral edges were then selected as start and end
points (Figure 3). Between these, 50 equally spaced slices
perpendicular to the line joining the two points were
created (Figure 4). A best fit axis was then defined to fit
the centres of these s lices (Figure 5). Applying a trans-
formation based on these axes, a coordinate f rame with
x-, y- and z-axes was defined. Several linear measure-
ments including clavicle length, width, thickness as well
Figure 1 Superolateral surface of the clavicle. Multiple points on
the superolateral flattest surface of the clavicle.
Figure 2 Best fit plane. Definition of a best fit plane.
Figure 3 Start and end points.Medialandlateraledgesasstart

and end points for slicing marked by dots.
Figure 4 Slicing. Equal slicing of the clavicle.
Daruwalla et al. Journal of Orthopaedic Surgery and Research 2010, 5:21
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as acromial and sternal angles were obtained using the
local coordinate frame [2]. These measurements later
assisted in describing the principal components of our
clavicle data with the acromial and sternal angles refer-
ring to the lateral and medial angle s described and
referenced above [2], respectively.
Statistical Shape Modelling of the Clavicle
Corresponding surface landmarks were established by
mapping points on the surface of one clavicle onto the
surface of each remaining clavicle in the study. First, the
origin and axes of the above mentioned local coordinate
frames of each clavicle were aligned. This methodology
was found to be reproducible in assessme nt by both the
same as well as different users. A set of sparse points,
acting as anatomical landmarks, was then defined on
one clavicle and an affine Iterative Closest Point (ICP)
transformation using specifically developed software in
Visualization Toolkit (VTK, Kitware Inc., New York,
USA) was used to register the points with each of the
remaining subject models (F igure 6, Figure 7). The clo-
ses t points to each of the registered surface points were
used to generate corresponding anatomical landmarks
on each subject model.
Using the corresponding surface lan dmarks, a statisti-
cal model of clavicle form was generated using Point
Distribution Modelling (PDM) [3]. The PDM technique

represents a training set of landmark data using the
mean landmarks and a set of eigenvectors which repre-
sent the linearly independent modes of variation (princi-
pal components) of the data set. Landmark data from
the training set can be approximated using the eigenvec-
tors corresponding to the largest eigenvalues l
i
.New
models can also be generated by transforming the mean
shape using the linearly scaled combinations of the most
significant eigenvectors. By applying a scaling limit of
3

i
the shapes generated will be similar to those in
the original training set. Unlike the approach taken by
Cooper et al [3], the subject models were not normal-
ised by size hence the PDM included both size and
shape variation.
Results of the principal component analysis (PCA)
comprised of size and shape components. A size compo-
nent reflects the variation in dimensions purely due to
size, with the ratios between dimensions remaining con-
stant while th e actual values of th e dimensions c hange.
This is identifiable as a principal component (PC) whose
coe fficients are of the same sign and similar magnitude.
Other PCs show variation in the shape of the clavicle
which is due to changing ratios between dimensions,
irrespective of size. Two clavicles are defined to be the
same shape if scaling, rotating and translating allows

them to occupy the same space.
Cluster Analysis
Cluster analysis is a technique used to categorize objects
into groups that share similar characteristics. Using the
k-means function from the MATLAB® Statistics Toolbox
[4], the clavicles were sorted into groups based on their
PC values. The correct numbers of clusters were deter-
mined by iterively varying k until the sum of the mean
Euclidean distance between each data point and the cen-
troid of the neighbouring clusters was maximized. Local
minima were avoided by performing the clustering pro-
cedure with several thousand replicates.
Results
The mean and standard deviations of the linear mea-
surements are illust rated below (Table 1). To simplify
the presentation of results, it should be noted that dia-
meter in table 1 refers to the mean of the width and
thickness measurements at the stated percentage
Figure 5 Opacity. Opacity reduced to show centres of each slice.
Figure 7 Regi stration of source and target models. Registration
of source and target models using aligned local coordinate frames
followed by affine ICP transformation.
Figure 6 Clavicle models. Source and target clavicle models.
Daruwalla et al. Journal of Orthopaedic Surgery and Research 2010, 5:21
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intervals. Table 2 shows the relationship between the
first four principal components and linear measure-
ments. These relationships are visually represented
below (Figure 8, Figure 9). The first principal compo-
nent (PC1) reflects the variation in clavicular length as

well as width and thickness at the midpoint. In our
study, this represented 70.5 percent of the variation.
Including the variation in lateral depth and angle
dimensions (PC2) defined and described using statistical
shape analysis [2], PC1 and PC2 in combination
accounted for 77.2 percent of variation in d imensions.
This increased to 82.2 a nd 86.4 percent with the addi-
tion of PC3 and PC4 which represented the variations
in medial depth and angle, and width and thickness
dimensions respectively. Finally, each clavicle was
approximated as a linear combination of the four PCs.
The range of PC values between genders is depicted
below (Figure 10). By analyzing these, differences are
noted between genders, most obviously in relation to
PC1 and PC4.
Using k-means clustering, clustering on a size basis
using PC1 resulted in two groups. The first included
five male clavicles and the second included all the
female clavicles and the remaining single male clavicle.
Clustering on a size and shape basis using all four PCs
resulted in five groups. The first of these groups
included four male clavicles, the second and third
Table 1 Mean and standard deviations of linear measurements.
Length/mm 10% Diameter/mm 50% Diameter/mm 90% Diameter/mm Sternal Angle/° Acromial Angle/°
Male Female Male Female Male Female Male Female Male Female Male Female
Mean 152.87 142.17 19.24 17.16 12.12 9.18 18.37 14.73 20.09 23.05 22.33 23.72
Std. Dev. 9.12 4.41 1.93 2.09 0.76 0.37 2.59 1.76 3.43 3.89 6.02 5.47
Table 2 Relationship between principal components and
linear measurements.
PC

1
PC
2
PC
3
PC
4
Length *-0.99 -0.07 -0.06 0.01
10% Diameter -0.38 -0.07 0.2 *-0.45
50% Diameter *-0.55 0.07 -0.09 *-0.73
90% Diameter -0.29 0.41 -0.31 *-0.46
Sternal Angle/Depth 0.37 0.13 *0.51 -0.12
Acromial Angle/Depth 0.32 *0.49 -0.28 0.08
% Variation 70.5 6.7 5 4.2
Statistically significant correlations (p < 0.05) indicated with *
Figure 8 Superior view of varying effects of principal components. Superior view of effects of varying the first four principal components of
the clavicle shape model individually.
Daruwalla et al. Journal of Orthopaedic Surgery and Research 2010, 5:21
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Figure 9 Dorsal view of varying effects of principal components. Dorsal view of effects of varying the first four principal components of the
clavicle shape model individually.
Figure 10 Comparison of principal components. Comparison of principal components showing range of values between genders.
Daruwalla et al. Journal of Orthopaedic Surgery and Research 2010, 5:21
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groupsincludedasinglemaleclavicleandthefourth
and fifth groups included six and nine female clavicles
respectively. The mean shape of each of these groups is
illustrated below (Figure 11).
Discussion and Conclusions
The application of principal component analysis (PCA)

allows the buildin g of statistical shape models of bone s
and joints. This has been used in conjunction with com-
puter assisted surgery in the past, examples including
the femur [5] and knee [6]. However, PCA of the clavi-
cle has not been performed.
Using PCA, interrelated variables are separated into
sets of linearly independent equation s [7]. As no statisti-
cally significant differences were observed between prin-
cipal components when comparing sides, our study
focused purely on gender-specific differences. By analyz-
ing PC values between men and women, it is clearly
seen that PC1 and PC4 are gender-related. The differ-
ence in the mean values of these PCs indicates that men
generally have longer clavicles that are t hicker and
wider at their midpo ints. These features are also found
to demonstrate greater variance in men. PC3, which
represents the sternal depth and angle, also indicates
gender-related differences with men again exhibiting
greater variance. Less sign ificant gender-related differ-
ence was noted in PC2, which represents the acromial
depth and angle.
By using k-means clustering, the clavicles were also
grouped on a size basis using PC1 and on a size and
shape basis with all four PCs. The silhouette value [8] of
a clustered data po int is a measure of how similar that
point is to points in its own cluster compared to points
in other clusters. The optimal number of clusters was
determined by varying k so the mean silhouette value of
the clustered data was minimized. Unlike a study in
2008 which stated that three types of modern human

clavicles exist [9], our k-means clustering results suggest
the possibility of at least fi ve morphological groups,
each composed solely of a single gender. However, it
must be stated that our findings were based on a limited
number of clavicl es and that an increased number
would be more desirable in order to support the pre-
sence of the five morphological groups we describe.
In our study, 70.5 percent of variation between mea-
surements is due to differences in width and thickness
at the midpoint as well as length, rather than shape. A
further 6.7 percent of variation is caused by difference s
in the lateral depth and angle dimensions and a subse-
quent 5.0 percent is due to differences in the medial
Figure 11 Morphological clavicle groups. Mean shapes of the five morphological groups of clavicles.
Daruwalla et al. Journal of Orthopaedic Surgery and Research 2010, 5:21
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depth and angle dimensions. Finally, a further 4 .2 per-
cent of variation is attributed to the change in width
and thickness. Although these four modes attribute to
almost 87 percent of clavicular variation, a single mode
attributes to 70.5 percent. This, together with the gen-
der-specific results evident using k-means clustering,
raises the question of how much variation must be
accounted for when designing an implant. Although
current clavicle fixation devices exist in a range of sizes
and shapes (Figure 12), none are gender-based designs.
Neither do the widths of current plates vary along their
length in order to closer fit the anatomic width variation
of clavicles (Figure 13), something previously studied [2].
And while many plates are pre-contoured to match the

natural s-shaped curve of the clavicle, they are only pre-
contoured in this single plane (Figure 12, Figure 14) and
do not take into a ccount the other curvatures or bow-
ings of the clavicle (Figure 11). While a larger sample
size is always more desirable and was limited in our
study secondary to the availability of cadaveric clavicles,
our findings support two issues that need addressing.
Firstly, the need for further research with regard to the
development of variable-shape as well as gender-specific
clavicle fixation devices. Perhaps more specifically for
men, who as previously mentioned, demonstrate a much
larger range of clavicle sizes and shapes. Secondly, and
Figure 13 Variation in clavicular width. Clavicular width (mm) measured at 10% intervals of total length from sternal end.
Figure 12 Examples of clavicle fixation plates. Example of a full range in size and shape of clavicle fixation plates.
Daruwalla et al. Journal of Orthopaedic Surgery and Research 2010, 5:21
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more importantly, varying the width across the entire
length of clavicle plates and pre-contouring them in
more than one plane would improve anatomic fit and
strength of the construct, these findings clearly support-
ing the soon-to-be-launched third generation clavicle
fixation plates by Acumed (Figure 15).
Acknowledgements
None.
Author details
1
Department of Orthopaedic Surgery, Beaumont Hospital, Dublin, Republic
of Ireland.
2
Department of Mechanical Engineering, University College

Dublin, Republic of Ireland.
Authors’ contributions
ZD designed the study and is primary author who performed the majority
of the research. PC performed statistical analysis and co-authored the
manuscript. CF developed the statistical software package in order to
perform shape analysis. DF assisted in the design of the study, supervised
the research, edited and evaluated the manuscript. HM assisted in the
design of the study, supervised the research, edited and evaluated the
manuscript and provided clinical relevance and guidance for the study. All
authors read and approved the final manuscript.
Competing interests
The authors declare that they have no competing interests.
Received: 5 November 2009 Accepted: 26 March 2010
Published: 26 March 2010
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doi:10.1186/1749-799X-5-21
Cite this article as: Daruwalla et al.: An application of principal
component analysis to the clavicle and clavicle fixation devices. Journal
of Orthopaedic Surgery and Research 2010 5:21.
Figure 15 Latest generat ion of clavicle plates.Exampleofa
newly developed range of clavicle fixation plates. Note the added
curvature of the implants in addition to the curve in the plane of
the natural s-shape.
Figure 14 Example of full fixation plates.Exampleofafullbut
lesser range in size and shape of clavicle fixation plates.
Daruwalla et al. Journal of Orthopaedic Surgery and Research 2010, 5:21
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